phguo / benderslib

Benders decomposition and its variants in Python

BendersLib: a Benders decomposition library

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BendersLib is a Benders decomposition library written in Python.

Supported Benders decomposition variants:

• Classical Benders decomposition
• Combinatorial Benders decomposition
• Generalized Benders decomposition
• Logic-based Benders decomposition

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1. Classical Benders decomposition

Classical Benders decomposition (BD) solves mixed-integer linear programming (MILP) with linear mixed-integer master problem and linear continues sub problem.

2. Combinatorial Benders decomposition

Combinatorial Benders decomposition (CBD) can handle 0-1 integer master problem and feasibility checking subproblem (a programming with objective function be set to 0).

3. Generalized Benders decomposition

Generalized Benders decomposition (GBD) solves nonlinear programming for which the subproblem is a convex program.

4. Logic-based Benders decomposition

Logic-based Benders decomposition (LBBD) can be used for problems which can be decomposed into any type of master and sub problem.

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Reference

1. Benders, J.F., 1962. Partitioning procedures for solving mixed-variables programming problems. Numer. Math. 4, 238–252. https://doi.org/10.1007/BF01386316
2. Codato, G., Fischetti, M., 2006. Combinatorial Benders’ Cuts for Mixed-Integer Linear Programming. Operations Research 54, 756–766. https://doi.org/10.1287/opre.1060.0286
3. Geoffrion, A.M., 1972. Generalized Benders decomposition. J Optim Theory Appl 10, 237–260. https://doi.org/10.1007/BF00934810
4. Hooker, J.N., Ottosson, G., 2003. Logic-based Benders decomposition. Math. Program., Ser. A 96, 33–60. https://doi.org/10.1007/s10107-003-0375-9
5. Rahmaniani, R., Crainic, T.G., Gendreau, M., Rei, W., 2017. The Benders decomposition algorithm: A literature review. European Journal of Operational Research 259, 801–817. https://doi.org/10.1016/j.ejor.2016.12.005